Instruction

1

Suppose we have two vectors that need to be folded up: the vector a and the vector b. To add two vectors in two ways: according to the triangle rule and the parallelogram rule.

2

The addition of two vectors according to the triangle rule.Set the start point. Swipe through this point, any of the vectors parallel transfer. Through the end of the constructed vector do a second vector parallel transfer. Connect the start point with the end of the second vector. On the segment connecting these points, put the arrow of the vector near the endpoint. You have found the desired vector that shows the sum of vectors a and b.

3

The addition of two vectors by the parallelogram rule.Set the start point. Parallel transfer from this point, draw

**vectors**a and b. You got the angle with the two sides. Extend it to a parallelogram: the end of the first guide vector for the second vector using the second vector of the first swipe.Swipe the diagonal of the parallelogram from the initial point. Specify the arrow. The total vector is found.4

The task of building the sum of three, four or more vectors is reduced to the task of building the sum of the two vectors. For example, to plot the sum of vectors a+b+c first, build the vector a+b, and then fold it with the vector c.

5

If you want to find the length of the resultant vector, it must first build (or find a picture constructed according to the problem). Further, it is necessary to solve the geometric problem to find the length using the available data.

# Advice 2 : How to calculate the vector

Vector as a directed line segment, does not only depend on the absolute value (modulus), which is equal to its length. Another important characteristic – direction vector. It can be defined as coordinates, and the angle between the vector and the coordinate axis. Vector calculation is also produced when finding the sum and difference of vectors.

You will need

- - definition vector;
- properties of vectors;
- calculator;
- - table Bradis or PC.

Instruction

1

To calculate a vector, knowing its coordinates. To do this, define the coordinates of the beginning and end of the vector. Let them be equal to (x1;y1) and (x2;y2). To make the calculation of a vector, find its coordinates. To do this, from the coordinates of end of vector, subtract the coordinates of its beginning. They will be equal to (x2 - x1;y2-y1). Take x= x2 - x1; y= y2-y1, then the coordinates of the vector will equal (x;y).

2

Determine the length of the vector. This can be done simply by measuring it with a ruler. But if you know the coordinates of the vector, calculate length. To do this, find the sum of squares of coordinates of the vector, and extract the resulting number square root. Then the length of the vector is equal to d=√(x2+y2).

3

Then find the direction vector. To do this, determine the angle α between it and axis OX. The tangent of that angle is equal to the y coordinate of the vector to the x-coordinate of the (tg α= y/x). To find the angle, use the calculator inverse tangent function, table Bradis or PC. Knowing the length of the vector and its direction relative to the axis, it is possible to find the position in space of any vector.

4

Example:

the coordinates of start vector is (-3;5) and the coordinates of the end (1;7). Find the coordinates of the vector (1-(-3);7-5)=(4;2). Then its length will be d=√(42+22)=√20≈4,47 linear units. The tangent of the angle between the vector and the axis OX will be tg α=2/4=0,5. The tangent of this angle is roughly equal to 26.6°.

the coordinates of start vector is (-3;5) and the coordinates of the end (1;7). Find the coordinates of the vector (1-(-3);7-5)=(4;2). Then its length will be d=√(42+22)=√20≈4,47 linear units. The tangent of the angle between the vector and the axis OX will be tg α=2/4=0,5. The tangent of this angle is roughly equal to 26.6°.

5

Find a vector that is the sum of two vectors whose coordinates are known. You should put the corresponding coordinates of the vectors that add up. If the coordinates of the vectors, which are formed, are respectively(x1;y1) and (x2;y2), their sum will be equal to the vector with coordinates ((x1+x2;y1+y2)). If you want to find the difference of two vectors, find the sum, pre-multiplying the coordinates of the vector which is subtracted by -1.

6

If you know the lengths of the vectors d1 and d2, and the angle between them α, find the sum, using the theorem of cosines. To do this, find the sum of the squares of the lengths of the vectors and from the resulting number, subtract twice the product of these lengths multiplied by the cosine of the angle between them. From the numbers, extract the square root. This will be the length of the vector that is the sum of these two vectors (d=√(d12+d22-d1∙d2∙Cos(α)).

# Advice 3 : How to add two vector

A vector is a directed line segment. Adding two vectors is like through geometrical or analytical method. In the first case, the result of addition is measured after the build, the second is calculated. The result of the addition of two vectors is a new vector.

You will need

- - the range;
- calculator.

Instruction

1

To construct a sum of two vectors, using parallel transport to align them so that they proceeded from a single point. Through the end of one of the vectors draw a straight parallel to the second vector. Through the end of the second

**vector,**draw a straight parallel to the first vector. Built straight will intersect at some point. With the right construction,**the vector**and the straight line segments between the ends of the vectors and the point of intersection will give a parallelogram. Build the vector, the beginning of which will be at the point of combination vectors and the end at the intersection of the constructed straight lines. This is the sum of these two vectors. Measure the length of the resulting**vector**with a ruler.2

If

**vector**parallel and pointing in the same direction, measure their length. Put them parallel segment whose length is equal to the sum of the lengths of these vectors. Point it in the same direction as the original**vector**. This will be their sum. If the**vectors**point in opposite directions, subtract their length. Draw a line parallel to the**vector**m point in the direction of the greater**vector**. This is the sum of oppositely directed parallel vectors.3

If you know the lengths of two vectors and the angle between them, find the module (absolute value) their amount is not generating the build. Calculate the sum of squares of lengths of vectors a and b, and add to it twice the product multiplied by the cosine of the angle α between them. From the resulting numbers, extract the square root c=√(a2+b2+a∙b∙cos(α)). This is the length

**of the vector**equal to the sum of vectors a and b.4

If

**vector**is specified coordinates, find their sum, adding the corresponding coordinates. For example, if a vector a has coordinates (x1; y1; z1), the vector b (x2; y2; z2), then folded pocino coordinates, obtain the vector c whose coordinates (x1+x2; y1+y2; z1+z2). This vector will be the sum of the vectors a and b. In the case when**vectors**are on the plane, the z coordinate is not taken into account.